Geometric Deep Learning: the Erlangen Programme of ML - Part 1
Staff - Faculty of Informatics
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Prof. Michael Bronstein, Università della Svizzera italiana, Imperial College London
For nearly two millennia, the word "geometry" was synonymous with Euclidean geometry, as no other types of geometry existed. Euclid's monopoly came to an end in the 19th century, where multiple examples of non-Euclidean geometries were shown. However, these studies quickly diverged into disparate fields, with mathematicians debating the relations between different geometries and what defines one. A way out of this pickle was shown by Felix Klein in his Erlangen Programme, which proposed approaching geometry as the study of invariants or symmetries using the language of group theory. In the 20th century, these ideas have been fundamental in developing the modern physics, culminating in the Standard Model.
The current state of deep learning somewhat resembles the situation in the field of geometry in the 19h century: On the one hand, in the past decade deep learning has brought a revolution in data science and made possible many tasks previously thought to be beyond reach -- including computer vision, playing Go, or protein folding. At the same time, we have a zoo of neural network architectures for various kinds of data, but few unifying principles. As in times past, it is difficult to understand the relations between different methods, inevitably resulting in the reinvention and re-branding of the same concepts.
Geometric Deep Learning aims to bring geometric unification to deep learning in the spirit of the Erlangen Programme. Such an endeavour serves a dual purpose: it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers, and gives a constructive procedure to incorporate prior knowledge into neural networks and build future architectures in a principled way. In this talk, I will overview the mathematical principles underlying Geometric Deep Learning on grid, graphs, and manifolds, and show some of the exciting and groundbreaking applications of these methods in the domains of computer vision, social science, biology, and drug design.
(based on joint work with J. Bruna, T. Cohen, P. Veličković)
Michael Bronstein received his Ph.D. degree from the Technion–Israel Institute of Technology in 2007. He has held visiting appointments at Stanford University, MIT, Harvard University, and Tel Aviv University, and has also been affiliated with three Institutes for Advanced Study at Technical University of Munich as Rudolf Diesel Fellow (2017–2019), at Harvard as Radcliffe fellow (2017–2018), and at Princeton (2020). He is a professor at USI Faculty of Informatics and Institute for Computational Science, professor at Imperial College London, where he holds the Chair in Machine Learning and Pattern Recognition, and Head of Graph Learning Research at Twitter. His main research expertise is in theoretical and computational methods for geometric data analysis, a field in which he has published extensively in the leading journals and conferences. He is credited as one of the pioneers of geometric deep learning, generalizing machine learning methods to graph-structured data. Michael is the recipient of multiple awards including five ERC grants, two Google Faculty Research Awards, Royal Society Wolfson Research Merit Award, and Dalle Molle Foundation Prize. He is a Fellow of the IEEE and the IAPR, ACM Distinguished Speaker, and World Economic Forum Young Scientist. In addition to his academic career, he is a serial entrepreneur and founder of multiple startup companies, including Novafora, Invision (acquired by Intel in 2012), Videocites, and Fabula AI (acquired by Twitter in 2019). He has previously served as Principal Engineer at Intel Perceptual Computing and was a key contributor to the RealSense 3D sensing technology.
Host: Prof. Cesare Alippi